The rails on a railroad are 30 feet long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in miles per hour is approximately the number of clicks heard in:
A. 20 seconds
B. 2 minutes
C. 1.5 minutes
D. 5 minutes
E. None of these
How to get a relation between the number of clicks and speed of the train and the time taken by it.
I assumed that the number of clicks has to be an integral value like 1,2,3..... Further i tried to figure out at what distance and at what time the train gives an integral value of the number of clicks. I tried to play with the options.But all in vain.
Let the required time be x hr. Speed when distance of one rail is taken is 30 ft / x hr. After converting in miles/ hr we get 0.00568 miles / x hr. So we want to know that at what time 0.00568 / x is the number of clicks heard according to question.
Now we know that we will only hear one click while travelling 30 ft so we want to know at what time 0.00568/ x equals 1 which means x = 0.00568 hence 0.00568 hr is the answer which when converted into seconds give almost 20 seconds.
So A is the answer.
30 ft (1 m/5280 ft) = .00568 mile
v = .00568 /T in hours
T in hours = .00568 /v
T in seconds = 3600*.00568/v
= 20.45/v
clicks/second = 1/T = v/20.45
so
v = 20.45 * clicks/second
1 click/second --> 20.45 mph
2 clicks/second -->41 mph
v = 20.45 * clicks/second
= clicks/20.45 seconds
so A.
To solve this problem, let's first determine the time it takes for the train to cover the 30-foot length of the rails.
We know that the speed of the train is given in miles per hour, so we need to convert the length of the rails to miles.
We can use the fact that 1 mile is equal to 5280 feet.
Therefore, the length of the rails in miles is 30/5280.
To find the time it takes for the train to cover this distance, we need to use the equation: time = distance/speed.
Let's first convert the given times to minutes:
A. 20 seconds = 20/60 minutes = 1/3 minutes
B. 2 minutes = 2 minutes
C. 1.5 minutes = 1.5 minutes
D. 5 minutes = 5 minutes
Now let's substitute the values into the equation:
A. time = (30/5280)/(speed in miles per hour)
B. time = (30/5280)/(speed in miles per hour)
C. time = (30/5280)/(speed in miles per hour)
D. time = (30/5280)/(speed in miles per hour)
From here, we can see that the number of clicks heard is determined by the time it takes for the train to cover the 30-foot length of the rails. We cannot determine the number of clicks based solely on the given times. Therefore, the answer is E. None of these.
See how many clicks in 1 minute at 60 mph
60*5280/30*60=176 clicks in 1 minute
But they want to know how many seconds for 60 clicks to occur:
60/176=About 1/3 of a minute, 20 seconds